Shropshire Council said an April launch would place it under “significant financial risk”.
Cabinet member David Vasmer said funds were provided for the purchase of vehicles, bins and the initial delivery, but the recent government financial settlement had “failed to provide any revenue funding for a weekly food waste service”.
South Derbyshire District Council spokesperson said the supplier of food waste collection vehicles was experiencing “exceptionally high demand”, making it difficult to get hold of them.
And East Hampshire District Council also confirmed availability of bin lorries was behind its delay, saying it did not yet have a date for when food waste collections would start.
Greg Ford, who lives in Buriton, East Hampshire, already separates his food waste for composting.
He said: “It makes you think about food waste, planning what to do with leftovers, so I think ironically collecting people’s food waste is going to cut down on food waste.
He added the council should take as long as it needed “to get it right”.